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2 years ago

How many solutions will there be to the following equation?16x^2=100

Mathematics

1 answer:

djverab [1.8K]2 years ago

4 0

Answer:

2 solutions; x=2.5 x=-25

Step-by-step explanation:

16x^2 = 100

x^2 = 100/16

x^2 = 6.25

x = (+-) sqrt 6.25

x = (+-) 2.5

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The points (1, 7) and (0, 2) fall on a particular line. What is its equation in slope-intercept form?

NARA [144]

Slope-intercept form is y = mx + b

So we can manage to do this:

(y - yo) = m.(x - xo)

Where (x, y) and (xo, yo) are points of this line, this way we can discover the slope.

(7 - 2) = m.(1 - 0)

5 = m

m = 5

So,

y = 5x + b

Now we still have to use (y - yo) = m.(x - xo), but this time we will put only 1 point and the slope.

(y - yo) = m.(x - xo)

(y - 2) = 5.(x - 0)

y - 2 = 5x

y = 5x + 2

So, this is the line in slope-intercept form.

4 0

3 years ago

\angle a∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 64^\circ64

Archy [21]

Answer:

If angle a and b are complementary angles, and angle a is 64, complementary equals 90, so 90-64= 26 degrees for angle b.

6 0

3 years ago

Read 2 more answers

Suppose that an object moves along the y-axis so that its location is y=x2+3x at time x. (Here y is in meters and x is in second

vfiekz [6]

Answer:

a) 13 m/s

b) (15 + h) m/s

c) 15 m/s

Step-by-step explanation:

if the location is

y=x²+3*x

then the average velocity from 3 to 7 is

Δy/Δx=[y(7)-y(3)]/(7-3)=[7²+3*7- (3²+3*3)]/4= 13 m/s

then the average velocity from x=6 to to x=6+h

Δy/Δx=[y(6+h)-y(6)]/(6+h-6)=[(6+h)²+3*(6+h)- (6²+3*6)]/h= (2*6*h+3*h+h²)/h=2*6+3= (15 + h) m/s

the instantaneous velocity can be found taking the limit of Δy/Δx when h→0. Then

when h→0 , limit Δy/Δx= (15 + h) m/s = 15 m/s

then v= 15 m/s

also can be found taking the derivative of y in x=6

v=dy/dx=2*x+3

for x=6

v=dy/dx=2*6+3 = 12+3=15 m/s

7 0

2 years ago

A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found

irakobra [83]

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

$H_0: p = 0.04$

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

$H_a: p > 0.04$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that $\mu = 0.04, \sigma = \sqrt{0.04*0.96}$

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that $n = 20, X = 0.1$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}$

$z = 1.37$

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

7 0

2 years ago

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If one ml. Equals one gram how much does a liter of water weigh

stich3 [128]

It will equal 1 Kg because 1ml = 1 gram

6 0

3 years ago

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